Average connectivity properties of wireless ad hoc networks

We consider the average radio coverage area size of a connected cluster /spl Omega/(/spl alpha/, r) in a uniformly randomly deployed wireless network over a D-dimensional infinite field (D /spl ges/ 1), where r is the radio distance, and /spl alpha/ the nodal deployment density. We show that /spl Omega//sub N/(y)=/spl utri//spl alpha//spl Omega/(/spl alpha/, r) is a function of y=/spl utri//spl alpha//spl Phi/(r) only, where /spl Phi/(r) denotes the volume of a sphere with radius r. We provide an explicit form of /spl Omega//sub N/(y) for arbitrary D as the sum of three terms, dominated by one that exhibits exponential behavior. For D = 1, we show that /spl Omega//sub N/(y) = exp (y/2) + (y/2) - 1. Our simulations validate our 1-d solution, and show that the exponent for 2-d deployment is smaller than y.